While .local does work with a lot of routers, many use other extensions as a faux hostname. Most will add that to the DNS search list, and if so you can find that by doing an nslookup glkvm.
For example, Google WiFi uses .lan, and Verizon's default routers use .mynetworksettings.com.
$ nslookup glkvm
Server: 127.0.0.53
Address: 127.0.0.53#53Non-authoritative answer:
Name: glkvm.mynetworksettings.com # This is the grep-able part
Address: 192.168.86.243